Small network Matlab code

Can someone help me with creating and manipulating this type of object in Matlab(top picture with red nodes): http://pages.physics.cornell.edu/~sethna/StatMech/ComputerExercises/SmallWorld/SmallWorld.html

[Jan]

Inputs should be: "Z/2" the number of short connections on both sides round the circle, "L" the number of red nodes and "p" the fraction of shortcuts.